%0 Journal Article
%T Non abelian cohomology of extensions of Lie algebras as Deligne groupoid
%A Yael Fregier
%J Mathematics
%D 2013
%I arXiv
%X In this note we show that the theory of non abelian extensions of a Lie algebra $\mathfrak{g}$ by a Lie algebra $\mathfrak{h}$ can be understood in terms of a differential graded Lie algebra $L$. More precisely we show that the non-abelian cohomology $H^2_{nab}(\mathfrak{g},\mathfrak{h})$ is $\mathcal{MC}(L)$, the $\pi_0$ of the Deligne groupoid of $L$.
%U http://arxiv.org/abs/1310.0959v1